Galaxy Clusters in the Line of Sight to Background Quasars:
I. Survey Design and Incidence of Mg II Absorbers at Cluster
Redshifts1
S. Lopez1 , L. F. Barrientos2 , P. Lira1 , N. Padilla2 , D. G. Gilbank3 , M. D. Gladders4,5 , J.
Maza1 , N. Tejos1 , M. Vidal1 , & H. K. C. Yee3
ABSTRACT
Quasar absorption line systems are redshift-independent sensitive mass tracers. Here we describe the first optical survey of absorption systems associated
with galaxy clusters at z = 0.3 − 0.9. We have cross-correlated quasars from
the third data release of the Sloan Digital Sky Survey with high-redshift cluster/group candidates from the Red-Sequence Cluster Survey. In a common field
of ≈ 20 square degrees, we have found 442 quasar-cluster pairs for which the
Mg II λλ2796, 2803 Å doublet might be detected at a transverse (physical) distance < 2 h−1
71 Mpc from the cluster centers. In addition, we have found 33 other
pairs in the literature and we have discovered 7 new quasars with foreground
clusters. To investigate the incidence (dN/dz) and equivalent-width distribution
n(W ) of Mg II systems at cluster redshifts, two statistical samples were drawn
out of these pairs: one made of high-resolution spectroscopic quasar observations
(46 pairs), and one made of quasars used in Mg II searches found in the literature
(375 pairs). The total redshift path from an ad-hoc definition of ’cluster redshift
path’ is ∆zcluster = 6.3 and ∆zcluster = 57.0 for the two samples, respectively. We
1
Departamento de Astronomı́a, Universidad de Chile, Casilla 36-D, Santiago, Chile.
2
Departamento de Astronomı́a y Astrofı́sica, Universidad Católica de Chile, Avenida Vicuã Mackenna
4860, Casilla 306, Santiago 22, Chile.
3
Department of Astronomy and Astrophysics, University of Toronto, 50 St. George Street, Toronto, ON
M5S 3H4, Canada.
4
Department of Astronomy and Astrophysics, University of Chicago, 5640 South Ellis Avenue, Chicago,
IL 60637, USA.
5
Visiting Associate, The Observatories of the Carnegie Institution of Washington, 813 Santa Barbara St.,
Pasadena, CA 91101, USA.
estimate the completeness level to be nearly 100 % for W detection thresholds
of W02796 > 0.05 and W02796 > 1.0 Å in the two samples, respectively.
The results are: (1) the population of strong Mg II systems (W02796 > 2.0 Å)
near cluster redshifts shows a significant (> 3σ) overabundance (up to a factor
of 15) when compared with the ’field’ population; (2) the overabundance is more
−1
evident at smaller distances (d < 1 h−1
71 Mpc) than larger distances (d < 2 h71
Mpc) from the cluster center; and, (3) the population of weak Mg II systems
(W02796 < 0.3 Å) near cluster redshifts conform to the field statistics. Unlike in
the field, this dichotomy makes n(W ) in clusters appear flat and well fitted by a
power-law in the entire W -range. We assess carefully all possible selection and
systematic effects, and conclude that the signal is indeed due to the presence of
clusters. In particular, a sub-sample of the most massive clusters yields a stronger
and still significant signal. Since either the absorber number density or fillingfactor/cross-section affects the absorber statistics, an interesting possibility is
that we have detected the signature of truncated halos due to environmental
effects. Thus, we argue that the excess of strong systems is due to a population
of absorbers in an overdense galaxy environment, and the lack of weak systems
to a different population, that got destroyed in the cluster environment.
Finally, comparison with models of galaxy counts show that there is proportionally less cold gas in more massive clusters than in low-mass systems, and two
orders of magnitude less Mg II cross-section due to weak systems than due to
stronger systems.
Subject headings: galaxies: clusters: general — quasars: absorption lines
1.
Introduction
Galaxy clusters trace the densest environments in the Universe. They thus constitute
the best laboratories to study galaxy evolution since (1) they contain a large number of
galaxies at essentially the same cosmic time, (2) their environment is extreme compared to
the field so galaxy transformations are constantly present, and (3) they can be traced to large
lookback times. Yet the baryon budget in clusters is not all that well constrained mainly
because it is not clear whether all baryonic constituents have been identified and quantified
1
This paper includes data gathered with the 6.5 meter Magellan Telescopes located at Las Campanas
Observatory, Chile.
(e.g., Ettori 2003; McCarthy, Bower, & Balogh 2007). According to Ettori (2003) these
constituents are: hot baryons (intracluster medium, 70%), cold baryons (galaxies, stars and
gas, 13%), and warm baryons (unknown, 17 %).
In addition to detecting galaxies and the intracluster medium in emission, clusters have
recently been probed through absorption by metals in x-ray spectra of background AGNs
(Takei et al. 2007). However, this absorption is rather associated with the hot intracluster gas
and not with the cluster galaxies. Since gas associated with field galaxies is known to produce
detectable EUV absorption in background quasar spectra, one could in principle probe the
cold-warm (T < 105 K) gas associated with cluster galaxies using this quasar absorption line
(QAL) technique. One great advantage of the QAL technique is that it provides a sensitive
measure of the gas that is independent of redshift and host-galaxy brightness.
In this paper we present the first spectroscopic survey of background quasars having
foreground clusters in the line of sight. The survey is aimed at probing metal absorbers
possibly associated with the cluster galaxies. We concentrate on the incidence of the redshifted Mg II λλ2796, 2803 Å doublet, an excellent tracer of high-redshift galaxies (Bergeron
& Stasinska 1986; Petitjean & Bergeron 1990; Steidel & Sargent 2002; Churchill et al. 2000;
Zibetti et al. 2007) for which extensive field surveys exist. The Mg II doublet has been used
extensively in spectroscopic quasar surveys because it is a strong and an easy-to-find transition, and has a redshift coverage from the ground of zabs & 0.2, matching imaging studies.
Redshifted metal absorption lines in a quasar spectrum appear together with absorption by
neutral hydrogen in what is called ’absorption systems’. The incidence of absorption systems, dN/dz, i.e., the probability of line-of-sight (LOS) intersection per unit redshift, and
d2 N
, are important observables as they depend both on
its equivalent width distribution, dW
dz
the absorbing cross-section and number density of the absorbers. More importantly, these
quantities can be measured without previous knowledge of the nature and environment of
the absorbers, i.e., galaxies, Lyα forest, etc.
Early Mg II surveys (e.g., Lanzetta, Turnshek, & Wolfe 1987, Tytler et al. 1987, Steidel
& Sargent 1992), sensitive to a rest-frame equivalent width (rEW) threshold of W02796 > 0.3
Å, established a population of non-evolving absorbers up to z = 2 with signs of clustering
on scales < 500 km s−1 (Petitjean & Bergeron 1990; Steidel & Sargent 1992). More recent
surveys (Churchill et al. 1999 [hereafter CRCV99]; Nestor, Turnshek & Rao. 2005 [NTR05];
Nestor, Turnshek & Rao 2006 [NTR06], Narayanan et al. 2007, Lynch, Charlton & Kim
2006; Prochter, Prochaska, & Burles 2006 [PPB06]) have shown a clear dichotomy between
strong and weak absorbers: the equivalent width distribution is steeper for weak systems
than for strong ones, with a transition around W02796 ≈ 0.3 Å. This has led some authors to
propose different populations/environments for these two classes of systems (NTR06).
On the other hand, surveys of galaxies selected by Mg II-absorption have shown a
population of normal morphology, bright galaxies, with absorption cross sections that range
from a few to several tens of h−1
71 kpc depending on rEW. Mg II was linked to bright galaxies
early in the 90’s thanks to the work by Steidel & Sargent (1992), Bergeron & Boissé (1991),
Lanzetta & Bowen (1990), Le Brun et al. (1993), among others, and more recently to rotating
disks (Steidel et al. 2002), neutral gas (Ellison et al. 2004a; Rao, Turnshek & Nestor 2006),
and also to large-scale structure (Williger et al. 2002). Although it seems clear that Mg II
absorption arises in galaxies of a wide range of morphologies and luminosities (Kacprzak
et al. 2007), the majority of the strong systems could be associated with blue, starburst
galaxies (Zibetti et al. 2007) with high metallicties (Ellison, Kewley, & Mallén-Ornelas
2005). However, none of these identifications tells us where and through which processes
the absorption occurs in these galaxies. If the Mg II occurs in extended halos, the covering
factor may be less than unity, so the halos must be patchy (Churchill et al. 2005; Churchill
et al. 2007). Indeed, this “patchiness” may point out to alternative explanations like Mg II
systems being the high-redshift analogs of local HVCs; i.e., warm (104 K), massive (106
M⊙ ) and compact, pressure-confined clouds embedded in a hot halo but still virialized (e.g.,
Maller & Bullock 2004), or, alternatively, part of cool galactic outflows (Bouche et al. 2006
[BMPCW06]). In any case, and despite a yet unclear origin, there is overall consensus that
Mg II flags star-forming regions in a variety of galaxies.
Do cluster galaxies host Mg II absorbers? This question motivates the present paper.
Cluster galaxy properties are essentially different from field galaxies due to environmental
effects. While the general galaxy population shows a wide range of mass, morphology, gas
and stellar content, and halo sizes, some of these properties have been found to depend
strongly on their local galaxy density. For instance, in the morphology-density relation
(Dressler 1980) early-type galaxies are concentrated toward the cores of the galaxy clusters,
while late-type galaxies are found mainly in the lower density environments (’cluster suburbs’
or the ’field’). Similarly, the increasing fraction of blue galaxies in clusters with increasing
redshift –the Butcher-Oemler effect (Butcher and Oemler 1984)– was the first indication that
the population of galaxies evolved.
Thus, clearly, detecting and studying Mg II absorption in overdense regions like cluster
galaxies has a twofold potential. It provides constraints to fundamental field properties of the
absorption systems (clustering, halo masses, and the absorber-IGM connection); on the other
hand, it also provides independent clues to galaxy accretion and evolution in clusters, which
may become a key complement to radio observations of cold gas in local and low-redshift
cluster galaxies (Chung et al. 2007; Vollmer et al. 2007; Verheijen et al. 2007).
Our paper is organized as follows: we first describe the quasar-cluster correlations in § 2,
then we describe the spectroscopic quasar observations in § 3. In § 4 we define the samples
and explain the method to get the Mg II statistics in clusters, while in § 5 we present the
results. An assessment of survey completeness and biases is presented in § 6. Finally, we
summarize the results in § 7 and discuss the implications in § 8. Throughout the paper we
use a cosmology with (ΩM , ΩΛ ) = (0.27, 0.73) and H0 ≡ 71 h71 km s−1 /Mpc.
2.
Selection of quasar-cluster pairs
Our primary goal is to study the incidence of Mg II absorbers in galaxies associated with
cluster galaxies, and this over an as wide as possible range of line strengths. To this aim a
sample must be built that includes bright quasars (suitable for high-resolution spectroscopy)
close in projection to and at higher redshifts than the clusters.
We searched for potential quasar-cluster pairs in three ways: (1) search for known Sloan
Digital Sky Survey (SDSS) quasars in fields of cluster candidates from the Red-Sequence
Cluster Survey (RCS); (2) search for known or new quasars in fields of clusters from the
Chandra database; (3) search in the NASA/IPAC Extragalactic Database (NED) for quasars
close in projection to objects labeled as clusters or groups.
In the search we have imposed two broad criteria2 : (1) for each quasar-cluster pair we
require 0.2 ≤ zcluster ≤ zquasar , i.e., the redshifted Mg II doublet may be detected at the
cluster redshift, zcluster , and is observable from the ground; and (2) at zcluster the quasar
line of sight (LOS) lies within a transverse (physical) distance of d = 2 h−1
71 Mpc of cluster
coordinates (this distance was considered enough to probe well beyond the virial radius).
We will refer to these criteria as the “quasar-cluster” criteria.
2.1.
Cross-correlation of SDSS quasars and RCS clusters
We describe the cross-correlation of cluster candidates from the RCS with quasars from
the SDSS data release three (SDSS-DR3; Schneider et al. 2005). We do not use a later
release because most of the extant Mg II statistics were obtained using DR3 data.
The RCS (Gladders & Yee 2005) is a ∼ 100 square degree optical survey conducted at
CFHT and CTIO, aimed at finding galaxy clusters up to redshift of one with some sensitivity
to massive clusters to z ∼ 1.4. This survey has been carried out with observations in two
2
Further, tighter criteria are applied later when we describe the statistical samples in § 4
bands, R and z ′ , to obtain galaxy colors and thus to enhance the contrast between cluster and
field galaxies (Gladders & Yee 2000). The main goal of the survey is to measure cosmological
parameters through the evolution of the cluster mass function (Gladders et al. 2007).
The clusters have been selected from an overdensity in position, color and magnitude,
and their redshifts have been determined from the loci of the red-sequence in the colormagnitude diagram. The redshifts were estimated from Simple Stellar Population codes and
then calibrated through the comparison with spectroscopic redshifts for a sample at a wide
range of redshifts (Gilbank et al. 2007). Masses for the different clusters were determined by
using the optical richness measured by the Bgc parameter (Yee & Ellingson 2003), and the
relationship between Bgc and M200 (the mass interior to r200 , where the average mass density
is 200ρc ) in Yee & Ellingson (2003; see also Gladders et al. 2007). Spectroscopy shows that
the contamination of the RCS cluster sample, even at z ∼ 1, is less than 10% (Gilbank et
al. 2007; Barrientos et al., in prep.), and as low as 3% at lower redshifts (Blindert et al., in
prep.).
Note that the RCS cluster sample we use is an inclusive sample of all RCS cluster
candidates with no redshift restrictions (other than the natural ones imposed by the survey
design) and no richness cuts. Thus, it is likely less clean than the restricted best sample used
in the analysis of Gladders et al. (2007); however, the inclusion of all candidates maximises
possible overlap with the SDSS quasar sample.
Although covering basically different areas, the cross-correlation of RCS clusters with
SDSS quasars from DR3 yielded 442 quasar-cluster pairs that met the quasar-cluster criteria
−1
(113 for d < 1 h−1
71 Mpc and 36 for d < 0.5 h71 Mpc). These quasar-cluster pairs are
distributed in a common area of ≈ 20 square degrees. We will refer to this sample as the
“SDSS-RCS sample”. This sample contributes the vast majority of pairs used in the present
study. Later in this paper we select quasar-cluster pairs from a sub-sample of rich clusters.
Fig. 1 shows the transverse-distance and cluster-redshift distributions of the SDSS-RCS
sample. In the first one we plot the number of pairs found to have a given quasar-cluster
distance. To see that this distribution results from a random distribution of clusters and
quasars, we calculate the expected distribution (the stright line in the Figure) defining a
mean density as the total number of pairs divided by the area of a circle of radius 2 000 h−1
71
kpc. This comparison shows that all distances are well represented and that they roughly
follow a uniform distribution, which is important for the homogeneity of the survey. The
righthand panel of the Figure shows that the redshift distribution of Mg II systems found in
SDSS quasar spectra (thin line; PPB06) and that of the SDSS-RCS sample have considerable
overlap, meaning that our cross-correlation is well suited for searches of Mg II in cluster
galaxies.
The SDSS-RCS sample of 442 quasar-cluster pairs is composed of 190 quasars and 368
clusters. Therefore, there are on average ≈ 2 clusters per LOS, and ≈ 20 % of the clusters
are crossed by more than one LOS. Regarding observability, roughly 80 % of the quasars are
brighter than g = 20 mag, and ≈ 50 % of them are observable from Southern facilities.
2.2.
New x-ray selected quasars
Since both galaxy clusters and quasars are ubiquitous x-ray emitters, using archival
Chandra observations proved to be a successful way of selecting further targets for our
study.
From the Chandra database we selected all public observations under the science category ‘Galaxy Clusters’. We imposed a maximum declination of +20 degrees, and a Chandra
exposure time & 25 ksec to ensure significant detections of the quasar candidates. The clusters also had to have a determined redshift above z = 0.2. A final list of 29 observations
that met these criteria were retrieved from the archive.
Next, we identified point-like sources in the x-ray data. We looked for candidate quasars
located within a radius of . 5′ from the cluster central position. Since the observations were
aimed at the cluster centers, we did not have to worry about the degradation of the Chandra
point spread function with increasing off-axis distances. We then searched for optical pointlike counterparts to the x-ray sources in SDSS images and obtained their R and B magnitudes
from the APM catalog. Imposing the criteria R > 16 and B−R . 2.0, a total of 49 candidate
quasars were selected in 23 of the Chandra clusters. We will refer to this sample as the “x-ray
sample”.
2.3.
Pairs from the literature
A search in the NED was performed of quasars near RCS coordinates. Out of 7263
searches, 28 yielded quasars not found by the SDSS, that met the quasar-cluster criteria.
We will refer to this sample as the “literature sample”. In addition, 5 other quasar-cluster
pairs found in the literature were added to this sample. It is important to note that SDSS
clusters are not well suited for our study due to their lower redshift (z < 0.3; Koester et al.
2007).
3.
3.1.
Observations
Low-resolution spectroscopy
Low resolution optical spectroscopic follow-up observations of the quasar candidates
from the x-ray sample were carried out with the Wide Field Reimaging CCD Camera in
long-slit grism mode on the du Pont telescope at Las Campanas Observatory on March 30
and September 15-16, 2006. We used the blue grism, which gives a resolution of ∼ 3Å and
a wavelength range of ∼ 4700Å.
Sixteen candidates were observed with enough signal-to-noise ratio to determine emission redshifts, and out of these, 7 quasars were confirmed. Other counterparts corresponded
to Seyfert and star-forming galaxies, and a few stars (probably due to chance alignments).
Therefore, the technique of using x-ray data to find quasars gave a success rate of ≈ 45 %.
3.2.
High-resolution spectroscopy
Echelle spectra were obtained using the MIKE spectrograph on the Las Campanas Clay
6.5m telescope. We obtained 18 quasar spectra in three runs on March 18-19 and September
23-24 and 29-30, 2006. Twelve of the quasars are from the SDSS-RCS, 2 from the x-ray, and
4 from the literature samples. The target selection was based only on airmass and brightness,
i.e., without consideration of cluster redshifts. The observed sample represents ≈ 15 % of
the total number of available targets in the three samples.
Weather conditions were good but quite variable for two of the runs. Seeing ranged from
good (1′′ ) to excellent (0.6′′ ). We made best efforts to obtain a S/N ratio as homogeneous
as possible throughout the sample.
MIKE is mounted on the Nasmyth port and the slit orientation on the plane of the sky
is fixed. For long exposures, and despite a low airmass, this requires manual corrections to
keep the object centered on the slit, a task that proved feasible in general but difficult to
carry out for some mag ≈ 20 targets. For five of our targets we used integration times in
excess of 4 hours. All spectra were taken with a 1′′ slit and an on-chip binning of 2 × 3 pixels.
With this setup the final spectral resolution of our spectra was ≈ 12.0 and ≈ 13.5 km s−1
(FWHM) for the blue and red arms, respectively.
To extract the spectra we used our own pipeline running on MIDAS. The two-dimensional
echelle spectra were flat-fielded (using star spectra taken with a diffusor) and extracted optimally (fitting the seeing profiles and taking into account the spatial tilts introduced by the
cross-dispersing prisms). The orders were then calibrated with spectra of a Thorium-Argon
lamp (using typically 15-20 lines per echelle order) and the different exposures co-added
using a vacuum-heliocentric scale with ∆λ = 0.067565 and 0.1447107 Å for the blue and red
orders, respectively. Finally, the orders were normalized and merged. The spectral coverage
of each spectrum is λ = 3 350 to 7 480 Å. Table 1 summarizes the echelle observations.
4.
Sample Definitions and Redshift Path Density
In what follows we describe the various statistical samples drawn from the data. These
samples were derived from the data on absorbers (see Table 2) and clusters (Table 3). We
define the ’cluster redshift-path’ of the survey and the sample of ’hits’, or absorption systems
found in the cluster redshift-path (summarized in Tables 4 and 5).
4.1.
Sample of Mg II Absorption Systems
4.1.1. Mg II in High-resolution Spectra (Sample ’S1’)
The 18 MIKE spectra along with one UVES spectrum from the Literature Sample
define what we shall call the ’high-resolution sample’, hereafter ’S1’. As in previous highresolution surveys (e.g., Narayanan et al. 2007), we searched visually for Mg II systems in
S1 by carefully scanning redshift chunks all along the range of Mg II detectability, each time
plotting in velocity both doublet lines. We considered lines detected at the 3σ level or higher
in both doublet lines.
Table 2 presents the absorption line data (LOS up to entry 19 in S1). Absorption
redshifts are determined to within δzabs ∼ 10−4 . rEW were calculated using pixel integrations
with 1σ errors from propagated pixel variances. Lines within a velocity window of 500
km s−1 were considered one system, to conform to previous QAL surveys. Column ’zEW ’
displays the minimum redshift at which a line with W0 = 0.05 Å can be detected at the 3σ
significance level. This value was computed assuming the error in the observed rEW is given
by σW = FWHM/hS/Ni (Caulet 1989), which holds when the spectral resolution dominates
over the line width, as is our case. Since the spectra have increasing S/N with wavelength,
there is no need to define a maximum redshift for the sake of the rEW threshold.
We found a total of 44 systems with 0.015 < W0 (2796) < 2.028 Å, 4 of them with
W0 (2796) > 1 Å (LOS 5, 6, 15, and 18). Out of these 4, two are reported in the Mg II survey
by PPB06 (see below), and two are new.
4.1.2. Mg II in Low-resolution Spectra (Sample ’S2’)
Out of the 190 quasars in the SDSS-RCS sample, 144 form 375 pairs where a Mg II
system with 0.35 <zabs < 0.9 can be found. We shall call these quasars the ’low-resolution
sample’, hereafter ’S2’. Note that S1 and S2 are not disjoint, since several quasars in S2
were observed at high resolution.
To find Mg II absorbers in S2 we cross-correlated the sample with two extant SDSS
Mg II samples: the sample by PPB06, comprising 7421 absorbers with W0 (2796) > 1.0 Å,
and the sample by BMPCW06, made of 1806 absorbers with W0 > 0.3 Å. PPB06 surveys the
redshift range zabs ∼ 0.35 − 2.3 and BMPCW06 has zabs ∼ 0.37 − 0.8. Both samples resulted
from searches in DR3 spectra. In the cross-correlation we imposed the criteria zabs ≤ 1.42.
This limit is given by the highest cluster redshift in the SDSS-RCS sample (but note that
we will later restrict the statistical samples to much lower redshifts).
Out of the 144 quasars in S2, 22 are reported in PPB06 to show at least one strong
(W0 (2796) > 1 Å) Mg II system in the SDSS spectrum. Out of these, one is in a quasar
that is paired with a cluster at too low a redshift and was therefore excluded. Out of the
remaining 21 quasars in PPB06, two were observed at high resolution and therefore are also
included in S1. The remaining 19 quasars show 21 systems that are listed in Table 2 along
with absorption redshifts and rEW from PPB06 (LOS 20 and beyond). Let us emphasize
that the two systems in LOS 15 and 18 of S1 are reported also by PPB06, so there is a total
of 23 Mg II systems with W0 > 1 Å in S2 (in the LOS 15, 18, 20 and beyond) that were
reported by PPB06. The two other W0 > 1 Å systems in S1 (LOS 5 and 6) are not reported
in PPB06.
Out of the 144 quasars in S2, 5 are reported in BMPCW06 to show at least one Mg II
system with W0 > 0.3 Å in the SDSS spectrum. Out of these, 4 with W0 > 1 Å are in
the PPB06 sample (though 2 of these, 092746.94+375612 and 141635.78+525649, with rEW
differing by ≈ 30 %) and only one has 0.8 < W0 < 1.0 Å. We decided not to include this latter
system into our statistics because the redshift range surveyed by BMPCW06 is shorter than
we can probe with our quasar-redshift pairs. Therefore, only the PBB06 results were used in
our statistics. However, after calculating rEW values for the two systems with disagreeging
rEW in the two surveys, we decided —for these two particular systems— to use the values
reported by BMPCW06, which better match ours (this choice has consequences for the rEW
distribution below).
4.2.
Sample of Clusters and Survey Redshift Path
4.2.1. Cluster Redshift Intervals
Table 3 displays the cluster data for each LOS that contains absorption systems (same
numbering as in Table 2). The 19 quasar spectra in S1 define a sample of 46 clusters with
redshifts between zcluster = 0.173 and 1.085. Out of these, 37 are drawn from the SDSS-RCS
sample, 2 from the x-ray sample and 7 from the literature sample. In S2 all clusters come
from the RCS.
RCS cluster redshifts are photometric and estimated to within δz = 0.1 in this redshift
range (Gilbank et al. 2007)3. The other 9 clusters have spectroscopic redshifts and we will
assume δz = 0.01, which corresponds to ∆v = 2 000 km s−1 at zcluster ∼ 0.5. Since we will
analyze absorption systems with zabs ∼zcluster , our survey’s redshift path will be defined by
what we shall call ’redshift intervals’ around each quasar-cluster pair. These are in turn
defined as [zmin , zmax ], with zmin =zcluster −δz and zmax =zcluster +δz, unless zmin < zEW , in
which case we set zmin = zEW . This choice implies that every redshift interval in S1 permits
a > 3σ detection of a system with W0 > 0.05 Å (this choice has also consequences on survey
completeness as explained below in § 6.2). No cluster has zmax < zEW , so no redshift interval
was excluded from S1. Recall that, in general, the number of redshift intervals is not equal
to the number of clusters, since some clusters are crossed by more than one LOS.
For redshift intervals associated with S2 we set zEW = 0.35, which defines a rEW
threshold of W0min = 1.0 Å. With this cut, out of the 442 quasar-cluster pairs in the SDSSRCS sample, 375 remain in S2. These pairs are associated with 144 LOS. In Table 3 (LOS
20 and beyond) we show only clusters associated with the 19 quasars in S2, besides LOS 15
and 18, that show a Mg II system with W0 > 1 Å.
Fig. 2 shows a diagram of redshift intervals in each of the LOS. The LOS numbering is
the same used in Tables 2 and 3. Quasar emission redshifts are labeled with asterisks, Mg II
absorption systems with circles, and clusters with vertical lines. The thick lines depict the
cluster redshift intervals. The numbers below the thick lines are the LOS-cluster distance
(at zcluster ) in h−1
71 Mpc. LOS up to 19 belong to sample S1; LOS 20 to 38 to sample S2.
3
For simplicity we have firstly neglected the fact that the redshift accuracy of the RCS clusters is a
function of redshift, but address this later in § 5.4.2.
4.2.2. A New Definition of Redshift Path Density
In order to calculate the incidence of Mg II absorbers at cluster redshifts, zcluster , a
function must be defined that accounts for the probability of detecting the doublet at a
given redshift. In QAL surveys such a function is the Redshift Path Density g(Wmin, zi ),
which gives the number of sightlines (quasar spectra) in which an absorption system with
rEW W0 > W0min might have been detected at redshift z = zi (see, for instance, Eq. [1] in
Ellison et al. 2004a). Thus, in QAL surveys, g(Wmin, zi ) provides the redshift path sensitivity
of the survey and the total redshift path surveyed is given by:
∆z =
Z
∞
g(Wmin, zi )dz.
(1)
0
Since in the present analysis we are interested in the incidence of absorbers at cluster
redshifts, the following conceptual modification has to be introduced: the redshift intervals
defined in § 4.2.1, [zmin , zmax ], will be treated as if they were ‘quasar spectra’, regardless of
how many of them are present in one LOS. The reason for this choice is that having more
than one cluster in the same LOS and at similar redshifts (overlapping clusters) increases the
a priori probability of detecting an absorber in that particular LOS. Similarly, two different
LOS through the same cluster add twice to the overall redshift path.
We therefore define a ‘cluster redshift path density’, gc (W0min, zi , d), as the function that
gives the number of cluster redshift intervals within a LOS-cluster distance d, in which a
W0 > W0min Mg II system at redshift zi might have been detected4 . The cluster redshift-path
∆zcluster between any two redshifts z1 and z2 is thus
∆zcluster (W0min, z1 , z2 , d)
=
Z
z2
gc (W0min, z, d)dz.
(2)
z1
In Fig. 4 we show gc (z) for the two samples. Note that gc (z) is not only different for
each of the samples (because of different rEW thresholds) but also for each cut in distance.
Sample S1 provides a cluster redshift path between z = 0.2 and z = 0.9 of ∆zcluster = 6.3 for
d < 2 h−1
71 Mpc. This is the longest path available for searches of lines as weak as W0 = 0.05
Å. In the redshift interval [0.35,0.90] and for W0 > 1 Å, sample S2 provides a redshift path
of ∆zcluster = 57.0 for d < 2 h−1
71 Mpc. Overlaps represent ≈ 40 % of the total redshift path
for clusters at d < 2 but only ≈ 10% for d < 1 h−1
71 Mpc. These numbers are summarized in
Table 4.
4
Clearly, gc is also a function of δz, see § 5.4.2.
4.3.
Sample of Mg II absorbers at cluster redshifts: ’hits’
We shall call an absorber a ‘hit’ when zabs is in a cluster redshift interval. The function
Nhit =Nhit (z1 , z2 , W0 , d) is defined as the number of hits between redshifts z1 and z2 with a
given cut in rEW and distance. Nhit enters in the definition of dN/dz below. We recall
that (1) there may be more than one hit in one redshift interval (two absorbers in the same
LOS through the same cluster); (2) there may be more than one hit in one cluster (two
absorbers in different LOS through the same cluster); and (3) redshift intervals may overlap
(thus increasing the probability of getting a hit). Table 5 summarizes the hits for the two
samples and various cuts in rEW and d.
The following caveat must be considered: overlapping redshift intervals have no one-toone correspondence with hits; in other words, we lack information as of which one of the
overlapping clusters is responsible for the absorption. This degeneracy, however, has a minor
effect on the results by cluster impact parameter, since there are only two cases in the whole
sample (LOS 5 and LOS 14) where a hit occurs in two overlapping intervals, with one being
at d < 1 and the other one being at 1 < d < 2 h−1
71 Mpc. These particular hits were assigned
−1
to both statistics: d < 1, and d < 2 h71 Mpc.
4.4.
Redshift Number Density of Absorbers in Galaxy Clusters
To study the incidence of Mg II in cluster galaxies we define — similarly to an unbiased
QAL survey defined by W0min — the redshift number density of absorbers in galaxy clusters,
(dN/dz)c , as the number of hits per unit cluster redshift:
(dN/dz)c (W0 , z1 , z2 ) ≡
and its rEW distribution, nc (W0 ) ≡
per unit EW, such that:
Z
d2 N
,
dW dz
Nhits (W0 , z1 , z2 )
,
∆zc (W0 , z1 , z2 )
(3)
as the number of hits per unit cluster redshift
W2
nc (W0 , z1 , z2 )dW = (dN/dz)c .
(4)
W1
The errors are calculated assuming Poisson statistics, for which we use the tables in
Gehrels (1986).
These two observational quantities, (dN/dz)c and nc (W0 ) must be proportional to the
average number density of absorbers in a cluster, nc (z), and their cross-section, σc (z):
(dN/dz)c ∝ nc (z) σc (z) .
(5)
Although in general (dN/dz) has been used to study how absorbers evolve, our samples
are rather small and we just focus on a possible overdensity δ of absorbers with respect to
the field. We define
δ ≡ (dN/dz)c /(dN/dz)f ,
(6)
where (dN/dz)f is the incidence of systems in the field. We compare the two distributions measured in clusters with the following field Mg II surveys: NTR06 (MMT telescope
spectroscopy, spectral resolution FWHM ≈ 2.2 Å; rEW threshold W0min = 0.1 Å), NTR05
(SDSS EDR, FWHM ≈ 4 Å, W0min = 0.3 Å), CRCV99 (Keck HIRES, FWHM ≈ 0.15 Å,
W0min = 0.02 Å), and Narayanan et al. (2007; VLT UVES, FWHM ≈ 0.15 Å, W0min = 0.02
Å). Other surveys have redshift intervals that do not match ours (Lynch, Charlton & Kim
2006).
These surveys have found (1) that weak and strong systems show different rEW redshift
distributions: weaker systems are fitted by a power-law while stronger systems are better
described by an exponential, with the transition at W0 ≈ 0.3 Å. This effect would hint at two
distinct populations of absorbers (e.g., NTR05); (2) little evolution of any of the populations
between z ≈ 1.4 and 0.4 (Narayanan et al. 2007; Lynch, Charlton & Kim 2006). The nature
of weak (W0 < 0.3 Å) Mg II is not clear yet. It has been suggested that single-cloud systems
may have an origin in dwarf galaxies due to their abundances (Rigby et al. 2002) or to their
statistics (Lynch, Charlton & Kim 2006); they might also be the high-redshift analogs to
local HVCs (Narayanan et al. 2007, and references therein). Unfortunately, there exist only
few QAL surveys of weak Mg II systems, mainly due to the more scarce high-resolution data.
5.
Results: The Incidence of Mg II in Galaxy Clusters
In this section we present the results on (dN/dz)c and nc (W0 ) as observed in S1 (for
systems having W0 < 1.0 Å) and S2 (W0 > 1.0 Å). For both samples we analyze pairs with
d < 2 and < 1 h−1
71 Mpc separately, and we restrict the statistics to z < 0.9, where the cluster
sample is more reliable. Finally, we re-analize S2 taking into account two refinements of the
method, namely selection by cluster richness and the redshift-dependence of δz.
5.1.
W0 < 0.3 Å systems
The parameterization by CRCV99 of their Keck HIRES data implies (dN/dz)f = 1.41
at hzi = 0.65 for field systems with 0.02 < W0 < 0.3 Å at 0.4 < z < 1.4. This is consistent
with the results by Narayanan et al. (2007) at that redshift and in the same rEW interval
using UVES data.
For our redshift intervals having d < 1 h−1
71 Mpc we find (dN/dz)c = 1.20 ([0.37 2.70]
1σ c.l.) for 0.05 < W0 < 0.3 Å and binning in the range 0.2 < z < 0.9. Given that our
data are complete only down to W0 = 0.05 Å, we cannot compare directly with the value by
CRCV99. Therefore, we apply a downward correction to this value of 23.3 %, which is the
fraction of systems with 0.02 < W0 < 0.05 Å in the CRCV99 sample. After this correction,
the field value is (dN/dz)f = 1.09, which is in good agreement with (dN/dz)c . For the d < 2
h−1
71 Mpc sample we find a somewhat smaller value of (dN/dz)c = 0.79 ([0.29 1.64] 1σ c.l.)
that is however still consistent with the field measurement.
5.2.
W0 > 0.3 Å systems
Figure 5 shows the cumulative values of (dN/dz)c (and their 1σ errors) for systems
with W0 > 0.3 Å. We bin in the ranges 0.2 < z < 0.9 (top panels) and 0.35 < z < 0.9
(bottom panels). The top panels show results from sample S1 only (46 quasar-cluster pairs,
hzi= 0.550), while points in the bottom panels were calculated using sample S2 (375 pairs;
hzi= 0.625). The filled circles are for clusters at distances d < 2 h−1
71 Mpc from quasar LOS
−1
and the open squares represent clusters with d < 1 h71 Mpc (symbols are slightly shifted
in the x-axis for more clarity). The curves correspond to the fit by NTR05 to their EDR
data of field absorbers with 1σ limits calculated as described in the Appendix of their paper.
These fits are in excellent agreement with the SDSS data of field Mg II absorbers.
There is an overdensity of hits per unit redshift in clusters compared with the field
−1
population for d < 1 h−1
71 Mpc clusters; the d < 2 h71 Mpc sub-samples instead, are consistent
with the field statistics. In addition, the data show that δ is larger for stronger systems
(W0 > 2.0 Å) than for weaker systems. These two trends are more clearly seen in Table 5,
where we compare the measured value of (dN/dz)c with the field, for various rEW ranges
(using cosmic averages from different authors). Note that the confidence limits listed in the
Table for (dN/dz)c are 2σ only. The overdensity effect for d < 1 h−1
71 Mpc (W0 > 1 and
W > 2 Å cuts) is significant at the 99% level or slightly higher. For d < 0.5 h−1
71 Mpc we
also note the overdensity of stronger systems, though the effect here is only 1σ due to the
small number of hits.
5.3.
Mg II λ2796 equivalent width distribution
5.3.1. Stronger (Weaker) Systems in Clusters are (not) Overdense
Fig. 6 summarizes our main result. It shows nc (W0 ) and 1σ errors for Mg II systems
at d < 1 and d < 2 h−1
71 Mpc from a cluster. Data points with W0 < 1.0 Å result from
sample S1 only, while points at W > 1 Å are calculated using S2 only. The solid curve is
the exponential distribution n(W0 ) = N ∗ /W ∗ exp −W0 /W ∗ fitted by NTR06 to their MMT
data for W0 > 0.3 Å (114 Mg II systems, hzi= 0.589). The parameters are W ∗ = 0.511 and
N ∗ = 1.071 and the fit is in excellent agreement with their data having 0.5 . W0 . 3.0 Å
(see their Fig. 2). The dashed curve is the power-law fit, n(W0 ) = 0.55 W0−1.04 fitted by
CRCV99 to their Keck HIRES data. The power-law is in excellent agreement with their
W0 . 0.3 Å data and also with data by Steidel & Sargent (1992), but clearly overestimates
the MMT and SDSS/ERD data for larger W0 .
Fig. 6 confirms the excess of strong (W0 & 1.0 Å) Mg II systems near cluster redshifts,
when compared with the field population. On the contrary, the weaker systems (W0 . 0.3
Å) conform to the field statistics. Furthermore, this effect seems more conspicuous for the
−1
d < 1 h−1
71 Mpc sample than for the d < 2 h71 Mpc sample, which shows a slight overdensity
only for stronger systems. The weak systems are also consistent with other QAL surveys.
For instance, the results by Narayan et al. (2006) for the 0.4 < z < 1.4 range are in good
agreement with ours (their Fig. 7) even for our d < 1 h−1
71 Mpc sample, considering a 29.3 %
downward correction to their n(W0 ) values due to our smaller rEW range of [0.05,0.3] Å. On
the contrary, for d < 1 h−1
71 Mpc, nc (W0 ) is overabundant by a factor of ≈ 3 in the [1.0,2.0]
bin and ≈ 15 in the [2.0,3.0] bin (note Table 5 shows a comparison with NTR05). The latter
result is significant at the > 3σ level (assuming no errors in the field average).
Summarizing, stronger systems (W0 & 1.0 Å) are overdense in clusters; weaker systems
(W0 . 0.3 Å) are not. This makes nc (W0 ) appear flatter than n(W0 ) (on a log-log plot) and
much better fitted by a power-law, also in the large-rEW end, than by an exponential.
5.3.2. Is the Effect Real?
The different behaviour of strong and weak systems cannot be due to the different
redshift paths ∆zc of S1 and S2. If this were the case, the offset in (dN/dz)c should be equal
in the entire rEW range; however, we see that the statistics is affected differentially.
Another possible caveat is that an incomplete survey in the small-rEW end would as
well have an effect on the differential behaviour of n(W0 ) between weak and strong systems
(weaker lines are more difficult to find). However, the [0.05,0.3] bin has 4 absorbers in S1,
meaning that to get a factor of say 10 more systems per unit rEW in that bin we should
have missed 36 hits, which is quite unlikely (10−12 for a Poisson distribution).
The stronger effect seen for d < 1 when compared with d < 2 h−1
71 Mpc is clearly
influenced by the shorter redshift path in the former selection. Indeed, from Table 5 we see
that the transition from d < 2 to d < 1 h−1
71 Mpc, is more or less governed by the change in
∆zcluster (i.e., the number of hits do not change much). We take this as a possible evidence
that the data is sensitive to a typical cluster only at distances below 1 h−1
71 Mpc. Further
−1
support for this idea is that the d < 0.5 h71 Mpc overdensities, though at low significance,
do not scale with ∆zcluster .
Finally, let us note that our definition of δ and the large radial distances implied by
the photometric redshift accuracy (δz) imply that ∆zcluster may (and probably does) include
some level of contamination by field absorbers. Consequently, what the present cluster data
allows us to state is that regions that contain a cluster do show more strong absorbers than
the cosmic average, while for weak systems those regions are indistinguishable from the field.
5.4.
Refinements
5.4.1. Selecting by Cluster Richness
In the current analysis we have included all the objects in our RCS catalog, constraining
its significance to be greater than 3σ (Gladders and Yee 2000). This threshold is low enough
to detect almost all the clusters in the RCS areas, but presumably it also includes low
mass groups and even some spurious detections. On the other hand, this selection has the
great feature that allows us to cross correlate a large number of objects, but also it has the
drawback that any signal we detect in the absorption systems might be diluted by low mass
objects or spurious clusters.
In order to quantify the extent of this ’dilution’ we have selected a subsample of clusters
with a more stringent criteria given by a minimum richness (that translates into a minimum
mass). So far we have used sample S2 that has a median Bgc of 263 that translates into
a mass of ≈ 2.4 × 1013 M⊙ (Blindert et al., in prep.). Similar values are obtained for the
subsample having d < 1 h−1
71 Mpc.
The more restricted sample, which we call ’S2-best’ is required to have only clusters with
Bgc ≥ 350. This selection includes only 125 quasar-cluster pairs for an impact parameter of
13
at least 2 h−1
M⊙ .
71 Mpc, and a median Bgc of 488 that translates into a mass of 8.8 × 10
Similarly, we find a median Bgc of 478 for a d < 1 h−1
71 Mpc. As shown in Table 5, repeating
the analysis of hits using S2-best yields higher overdensities —by ∼ 50%— than for S2 for
the same rEW ranges. Most importantly, despite a much lower redshift path, the significance
of the result is still high (> 3σ).
Sample S1 has fewer quasar-cluster pairs and only a few of the clusters come from the
RCS sample. For these objects we find a median Bgc of 327 for an impact parameter of 2
Mpc and 258 for the smaller aperture, i.e., consistent with the larger sample. Therefore, a
similar analysis for S1 was considered not worth performing due to the few clusters in that
sample. However, we note that the median Bgc is not particularly low, so this sample is also
representative of more massive clusters (i.e., the lack of overdensity is not due to a chance
conjunction of low mass systems).
Concluding, finding a significantly stronger signal in clusters selected by a mass proxy
gives strong support to both the method and the reliability of the systems used in the
analysis. In fact, the richness selection not only provides more galaxies per clusters but
also picks up larger clusters. Both selection effects are expected to increase the a priori hit
probability.
5.4.2. Cluster Redshift Accuracy
Since our comparison between cluster and field Mg II statistics depends on the definition
of redshift intervals, we have to consider what effect the cluster redshift accuracy may have
on our results. For clusters with spectroscopic redshifts we have assumed δz = 0.01. If due
to the Hubble flow, this translates into a radial distance of 67 comoving Mpc; therefore,
one might want to shorten δz to overcome the problem of contamination by field absorbers.
Unfortunately, the redshift path provided by the pairs with spectroscopic cluster redshifts
represents only ≈ 2 % of ∆zcluster . Since shortening to δz = 0.005 does not exclude the only
hit (LOS 9) at a spectroscopic zcluster , (dN/dz)c remains practically unchanged.
The vast majority of our clusters have photometric redshifts and our analysis assumes
δz = 0.1 for those ones. This is indeed an over-estimate for the lower-redshift clusters,
zcluster . 0.5, where the accuracy can be as good as δz ≈ 0.04. In order to see whether a
smaller δz would affect the results on (dN/dz)c we use the parameterization δz = 0.04(1 +
zcluster ) and re-compute gc (z) and Nhits . Restricting the analysis to d < 1 h−1
71 Mpc pairs in
S2 (where the overdensity signal is most evident), we find that out of 7 hits with W0 > 1
Å only one hit (LOS 28, W0 = 1.58 Å) is ruled out due to the shorter redshift intervals.
Since the new δz makes the total redshift path between z = 0.35 and z = 0.9 decrease to
∆zcluster = 9.18, we find actually a higher overdensity of δ ≈ 4 and δ ≈ 10 for W0 > 1.0
and 1.0 < W0 < 2.0 Å, respectively. We conclude that our result is indeed affected by a
more precise parameterization of the RCS redshifts but such refinement makes the signal
even stronger. In order to avoid fine-tuning too many variables, we continue the analysis of
the results using a constant δz.
6.
Statistical Significance, Possible Biases, and Caveats
Despite the strong test provided by the mass selection, our method might still suffer from
possible systematics and biases hidden in the statistical properties of the various samples.
We analyze these in what follows.
6.1.
Statistical Significance
We start by asking whether the detected overdensity might be due to chance alignments.
To assess the statistical significance of the observed number of hits one might want to run
Monte Carlo simulations by creating samples of random cluster redshifts. However, this is
equivalent to calculating dN/dz from random sub-samples drawn from the parent quasar
sample (i.e., creating random RCS-SDSS samples). Such kind of simulations must, by definition, yield the cosmic value obtained by QAL surveys, a number against which we have
compared our resuls. To see whether we recover the expected number of field absorbers, we
calculate (dN/dz)f in the complementary redshift path of our quasar-cluster sample, that
is, the path that does not include clusters. If our sample is biased toward an overdensity of
absorbers for reasons other than the presence of clusters we should get an overdensity here
too; if it is not, we should recover the field value. We analyze quasars in sample S2, the
one that yields the overdensity, and split it into two redshift ranges: z =[0.35,0.9], the one
used to get (dN/dz)c , and z =[0.9,1.4]. The latter was not used in the analysis of cluster
absorbers but may be a useful check for unbiased LOS.
There are 85 quasars in S2 that provide cluster redshift intervals at d < 1 h−1
71 Mpc,
where W0 > 1 Å Mg II systems may be detected. Between z = 0.35 and 0.9 the total
quasar redshift path of this sample is ∆zquasar = 45.15, so the complementary redshift path
is ∆zfield = ∆zquasar − ∆zcluster = 45.15 − 14.13 = 31.02, where we have subtracted the cluster
path ∆zcluster = 14.13 (see Table 5).
The expected number of W0 > 1.0 Å systems along ∆zfield is thus 5+3.4
−2.2 and the expected
+1.9
number of systems with 2.0 < W0 < 3.0 Å is 0−0 (1σ errors). From Tables 2 and 5, the
observed number of systems along ∆zfield in this redshift range is: [# systems in RCS-SDSS]
− Nhits = 10 − 7 = 3 for W0 > 1.0 Å and 3 − 3 = 0 for 2.0 < W0 < 3.0 Å systems (i.e., no
system with 2.0 < W0 < 3.0 Å was expected in the field and no system was observed in the
field, with the 3 other systems all being hits). These values are in agreement with the field
expectation.
Repeating the above analysis for the z =[0.9,1.4] range, we get: ∆zquasar = 31.38,
∆zcluster = 3.00, number of expected field absorbers: 7+3.8
−2.6 , number of detected field absorbers:
8 (total) - 1 (hit) = 7, i.e., again within the field expectation. We conclude that the observed
overabundance of strong Mg II systems is not due to chance alignments and must reflect
real overdensities. In other words, sample S2 of quasars is biased only by the presence of
clusters. The bias vanishes at redshifts other than zcluster , where we recover the cosmic
statistics obtained in QAL surveys (the presence of clusters in these surveys has negligible
influence on such statistics).
6.2.
Yet More Possible Biases and Caveats
6.2.1. Clusters and Quasars
Besides the obvious fact that the completeness of our cluster sample — drawn mainly
from the RCS — depends on the RCS algorithm, it is important to stress that the parent
cluster and quasar samples are totally independent each from the other. The RCS sample
is certainly not complete for S2 (particularly at higher redshifts), which includes low mass
systems, but it is for S2-best up to z . 1, which includes moderately massive clusters. On
the other hand, the SDSS quasar sample should be ∼ 90 % complete (York et al. 2000).
These and the arguments given in § 2.1 lead us to conclude that the SDSS-RCS sample, and
thus also sample S2-best of pairs, is complete and homogeneous, at least at the same level
as their parent surveys.
Another obvious strength of the quasar-cluster sample is that the search of absorbers
in S2 (PBB06; BMPCW06) was performed independently of our selection. This is not
completely true for S1 since those quasars were selected for follow-up spectroscopy after the
quasar-cluster selection. However, at the telescope, the targets were selected without prior
knowledge of cluster redshifts; moreover, even if this had been the case, the low-resolution
spectra provided by the SDSS do not permit an a priori selection of weak systems. Therefore,
there was no way to prefer quasars with absorbers. We discuss this further below in the
context of absorber statistics.
Finally, the following caveat must be mentioned: brighter quasars are chosen for spec-
troscopy, which might be amplified by gravitational lensing by the absorber host galaxies
(see discussion in § 8).
6.2.2. Absorbers
Surveys of quasar absorption-line systems assess the completeness of the samples via
cumulative ∆z as a function of rEW threshold (Steidel et al. 1992). Since we have chosen
our redshift path to include only spectral regions sensitive to W0 > 0.05 Å, we consider
the sample S1 of absorbers to be nearly 100% complete. Similarly, we assume that S2 is
statistical in the sense that all Mg II systems with W0 > 1.0 Å were listed in PPB06, who
argue that their search is > 95 % complete.
As for the homogeneity of the samples, we have kept S1 and S2 carefully separated.
Again, out of the 4 W0 > 1 Å systems found in S1, we have considered in S2 only those two
found by PBB06 (including the remaining two would increase δ since one system is a hit).
Admittedly, one concern is that detecting an overdensity in one sample and not in the
other may reflect a hidden systematic. We do not have at this time the means of testing such
possible systematics. If we use only S1 in the W0 > 1 Å range we also find an overdensity
with respect to the field, although with low significance: 1 hit is expected while 2 are found.
However, as pointed out above, these statistics may be influenced by the fact that quasars
in S1 were selected as having a cluster in the LOS, and strong systems are readily seen in
the SDSS spectra. However, weak systems are not seen in the SDSS and we know they
do not cluster around stronger systems (CRCV99). In addition, if there were in fact such
hidden systematics, why is not the supposedly biased sample (S1) the one that shows the
overdensity? In other words, despite an obvious selection effect toward targets with clusters,
S1 does yield the field statistics for weak absorbers.
Finally, note that the significance of our result for strong absorbers could increase if a
larger cluster redshift path were surveyed. Tables 4 and 5 show that only roughly 3 − 4% of
the quasar-cluster pairs results in hits. This explains why an earlier attempt failed to detect
strong Å Mg II systems in a sample of 6 Abell clusters (Miller, Bregman & Knezek 2002).
7.
Summary of the Results
We have cross-correlated candidate galaxy clusters from the RCS at zcluster = 0.3–0.9
with background quasars from the SDSS DR3 to investigate the incidence (dN/dz)c and
rEW distribution nc (W0 ) of Mg II absorption systems associated with cluster galaxies. We
have found 442 quasar-cluster pairs at impact parameters d < 2 h−1
71 Mpc from cluster
coordinates, where Mg II might be detected in redshift regions ±0.1 from a cluster. The
cluster sample contains all systems in the RCS, and is dominated by low-mass clusters and
groups with hMi ∼ 2 · 1013 M⊙ cluster candidates. We have defined a cluster redshift-path
density in terms of the quasar-cluster pairs. Using extant surveys of strong Mg II systems
in DR3 quasar spectra and our own follow-up high-resolution spectroscopy, we calculated
(dN/dz)c and nc (W0 ) for the rEW range 0.05 < W0 < 3.00 Å. The results were:
1. There is an excess of strong (W02796 > 1.0 Å) Mg II absorbers near —i.e., at similar redshift of and close in projection to— galaxy clusters when compared to surveys in the field. The effect is significant at the 2σ level. This overdensity, δ ≡
(dN/dz)c /(dN/dz)f , is also more pronounced at smaller distances (d < 1 h−1
71 Mpc)
−1
than at larger distances (d < 2 h71 Mpc) from the cluster, which we interprete as a
dilution of the effect in the field. On the other hand, the excess is also more pronounced
for stronger systems. For d < 1 h−1
71 Mpc and W0 = [2.0,3.0] Å, we measure δ ≈ 6–15
(depending on the field survey used for comparison), and the significance increases to
3σ.
2. If we select the sample third with most massive (and significant) cluster candidates,
we find the excess of absorbers increases by 50% for the sub-sample dominated by
hMi ∼ 1014 M⊙ clusters. The effect becomes also more significant, rendering reliability
to our detection.
3. The weak population of Mg II systems (W0 < 0.3 Å) in clusters conform to the field
statistics. The absence of an overdensity is not due to lack of sensitivity. This effect
and the excess of strong systems make nc (W0 ) appear flatter on a log-log scale, so
—contrary to the field— it can be fitted by a power-law over the whole range of rEW.
8.
Discussion
The most obvious interpretation for the observed overdensity of strong absorbers is
that clusters represent a much denser galaxy environment than the field: an overdensity is
expected if field and cluster galaxies share the same properties responsible for the Mg II
absorption. Below we discuss this possibility and then hypothesize on why this trend is seen
only for the strong cluster absorbers (thus producing a flatter rEW distribution than in the
field). Finally, we assess the implications for the fraction of cold gas in galaxy clusters.
One evident caveat to have in mind in comparing cluster and field properties of Mg II is
that possible correlations between rEW and galaxy properties (colors, absorber halo mass,
dust redenning and gravitational lensing) all have been studied in the framework of the
overall population of absorption systems. Such field properties do not necessarily hold for
clusters, and any departure due to cluster environments may have not been detected in the
field studies.
8.1.
Galaxy Overdensity
In order to see whether the observed overdensity of strong absorbers, δ, is consistent
with a model of evolution of structure a detailed numerical simulation is necessary, which is
out of the scope of the present paper and will be presented elsewhere (Padilla et al., in prep.).
However, a crude estimate of the expected (dN/dz)c can be obtained from semi-analytical
models. We start assuming field and cluster absorbers share the same Mg II cross section, σ.
In this case, from Eq. 5, δ is proportional to the average volume overdensity of galaxies in a
cluster, δg . To calculate δg , we assume that galaxies are spatially distributed in the same way
as the dark matter, and therefore adopt a NFW density profile (Navarro, Frenk & White,
1997), which depends on the total mass of the cluster of galaxies. We then calculate δg within
1 and 2 h−1
71 Mpc from the cluster center, for masses corresponding to the range present in the
RCS sample. Given that the LOS will actually cross different density amplitudes as it passes
through a cluster, we simply make an order of magnitude approximation and take half the
actual overdensity at the impact parameter. The number density of galaxies within a cluster
of galaxies is obtained assuming a Halo Occupation number corresponding to a magnitude
limit of Mr(AB) = −17, which states that the number of galaxies populating dark-matter
halos of a given mass is (Cooray 2006)
N=
1
exp(β ∗ (Mmin − M)) + 1
+ 10α∗(M −M1 ) ,
(7)
whith Mmin = 1011.77 h−1 M⊙ , M1 = 1012.96 h−1 M⊙ , α = 1.04, and β = 99. We then calculate
the average density of galaxies above the same magnitude limit by populating all haloes in the
Millenium simulation (Croton et al. 2006) using this same prescription, and then counting
the total number of galaxies and dividing this by the total volume of the simulation.
The results for later-type galaxies are displayed in Table 6. Note that this estimate for
δg includes only the cluster region; thus, it is to be compared with δ − 1, i.e., the overdensity
of absorbers after subtracting the field contribution.
8.2.
W0 & 1.0 Å Absorbers
8.2.1. Absorber Overdensity
If we first concentrate on moderate mass clusters, M ∼ 2·1013M⊙ , which vastly dominate
sample S2, we see the expected overdensity of cluster galaxies is quite in line with δ − 1,
the observed absorber enhancement, for d < 1 and d < 2 h−1
71 Mpc (using for S2 fiducial
values of δ = 2 and δ = 10 for the two apertures, respectively; see Table 5). In other words,
the probability of hitting a Mg II galaxy in a cluster is the same as in the field. Note that
this does not imply that quasar LOS do not ’see’ the foreground clusters but rather that
this probability scales with galaxy overdensity. The observed match between δg and δ − 1
supports the hypothesis that strong absorbers in less masive clusters and in the field share
similar properties.
The situation seems different for sample S2-best, which is dominated by more massive,
M ∼ 1014 M⊙ , clusters. There we find that the absorber overdensity is enhanced by a factor
of . 2 with respect to that one in less massive clusters. On the other hand, from Table 6
we see that the more massive clusters provide a factor of 5 more galaxies than less massive
ones. Therefore, the overdensity of galaxies in massive clusters overpredicts the overdensity
of strong absorbers by a factor of ≈ 2-3. We infer that —on average and neglecting other
effects, see next Section— the total cross-section of strong absorbers must be smaller in more
massive clusters than in the field by a factor of ≈ 2-3.
It is tempting to draw conclusions also for d < 0.5 h−1
71 Mpc, despite the less significant
signal observed in the absorber statistics. For both mass ranges, the expected overdensity
−1
of galaxies increases by a factor of ≈ 4 comparing the < 1 h−1
71 Mpc and the < 0.5 h71 Mpc
apertures. Again assuming same properties as in the field, the absorbers statistics fails to
reproduce such increase by that same factor of 4 (since roughly the same δ is observed for
d < 1 and d < 0.5 h−1
71 Mpc). This could indicate the gas cross section is even smaller at
distances closer than half Mpc to the cluster center (although the factor 4 is still within 95%
confidence limits).
8.2.2. Gravitational Lensing
Although we will present elsewhere a study of gravitational lensing by the cluster galaxies
in our sample, this effect deserves a few words here since it may have direct implications
for (dN/dz)c . We are particularly interested in lensing magnification by the RCS galaxies
and the possible bias it may have introduced in the SDSS sample used here. Inclusion of
magnified quasars in magnitude-limited surveys like the SDSS might increase the number
of (lens) absorbers per unit redshift (1997 Bartelmann & Loeb 1996; Smette, Claeskens &
Surdej).
Lensing magnification has been reported not to induce a significant effect on the field
statistics of strong Mg II systems (as observed in SDSS quasar spectra; Menard et al. 2007).
However, in our case the probability of strong lensing might be greatly enhanced due to
not only the quasar light crossing the densest galaxy environments, but also to a possible
combination of cluster/quasar redshift ratios of 1:2 that maximizes the probability of strong
lensing for zem ∼ 1 (indeed, that probability is maximal at zlens ∼ 0.7 for zem & 2). Statistical
overdensities of bright background quasars (or paucity of faint quasars) associated with
foreground clusters or large structure have been already detected (Myers et al. 2003; Scranton
et al. 2005; but see Boyle, Fong & Shanks 1988). However, when searching for the lensing
galaxies, one finds that the majority of them are early-type (e.g., Fassnacht et al. 2006)
which are not expected to host strong Mg II absorbers (Zibetti et al. 2007). We conclude
that a great impact of lensing on δ should not be expected. Nevertheless, if a fraction of
these lensing galaxies indeed does act as strong Mg II absorbers, then (dN/dz)c observed in
our sample might be partly due to lensing. In such a case, the values quoted in § 8.2.1 for
the fractions of Mg II cross section that is expected from galaxy counts but not observed
in absorption must be seen as upper limits, since they result from a sample that is biased
toward more lensing absorbers.
8.3.
W0 . 0.3 Å Absorbers
8.3.1. A flatter rEW Distribution for clusters
In contrast with strong systems, we do not detect an overdensity of weak absorbers in
clusters, although our survey is sensitive enough in the W0 < 0.3 Å range. As already stated,
this dichotomy induces a flatter, more uniform, rEW distribution than what is observed in
the field, where weak absorbers have a much steeper distribution than strong absorbers.
Does this mean that neither gravitational lensing nor galaxy overdensity influence the weak
absorber statistics? Since lensing magnification is a strong function of Mg II rEW (Bartelmann & Loeb 1996), (dN/dz)c [W0 < 0.3Å] is perhaps insensitive to lensing. However, it
would be unlikely that also the galaxy excess that clusters represent had no influence on
the incidence of the weak absorbers. This would require a physically distinct population
of cluster absorbers, detached from the strong absorbers, that does not scale with galaxy
overdensities.
Alternatively, since either the absorber number density or filling-factor/cross-section
affect the (dN/dz)c statistics, an interesting possibility is that we have detected the signature
of processes giving rise to Mg II absorption (gas outflows or extended halos, the two current
compelling scenarios) that are at play in clusters in a different way than in the field. For
instance, if we consider the extended halo hypothesis (Churchill et al. 2005), the low rate
of weak Mg II absorbers we observe in clusters might be due to truncated halos due to
environmental effects. Such an effect is expected if cluster galaxies lose their gas after a
few orbits in processes like galaxy harassment and/or ram pressure stripping (Mayer et al.
2006), and it has actually been observed in 21cm observations of low-redshift (Giovanelli
& Haynes 1983; Chung et al. 2007; Verheijen et al. 2007) and local (Bravo-Alfaro et
al. 2000) clusters. Interestingly, ram pressure affects mostly less-massive galaxies; on the
other hand, according to some authors weaker systems seem to arise in under-luminous,
less-massive galaxies (Churchill et al. 2005; Steidel et al. 1992). All this fits well with the
lack of absorbing cross-section observed here for cluster galaxies associated with weak Mg II
absorption.
If we instead consider the weak absorbers to be individual, small ’clouds’ that are
distributed more densely toward the centers of galaxies, then weak Mg II arises in sightlines
through the outer parts of a galaxy (e.g. Ellison et al. 2004b). This is supported by the
typical sizes of strong/weak Mg II which are an order of magnitude different (Ellison et
al. 2004b). If the strong Mg II systems arise in the centers of galaxies, then the cluster
environment does not affect them, so that their observed overdensity traces the overdensity
of cluster galaxies (with gas). However, the weak Mg II population get destroyed in the
cluster environment, and the fact that we do not detect an overdensity for them simply
reflects that the field contamination dominates in our redshift path.
Our observations allow us to put limits on the shortage of total cross-section for weak
systems. If the flat rEW distribution is due to truncated halos, the excess of galaxy counts
in Table 6 correspond to the missing fraction in absorbing cross section. We then conclude
that there is between one and two orders of magnitude less total cross-section of Mg II gas
having W0 < 0.3Å.
8.4.
Clustering
Several studies have shown that strong (W0 & 1.0) Mg II absorbers trace overdense
regions. For example, Cooke et al. (2006) found that damped Lyα (DLA) systems cluster
like LBGs, which themselves have a non-negligible clustering signal. DLA systems also cluster around quasars (Ellison et al. 2002; Russell, Ellison & Benn 2006; Prochaska, Hennawi
& Herbert-Fort 2007), just as galaxies cluster around QSOs, and also around themselves
possibly revealing large-scale structure (Lopez & Ellison 2003; Ellison & Lopez 2002). More
recently, Bouche et al. (2007) have found clustering of strong Mg II systems around luminous
red galaxies (LRGs).
At first glance our interpretation of gas truncation affecting only weak absorbers seems
to go in the opossite direction of the results by Bouche et al. (2007). These authors find that
LRGs correlate more strongly with weak Mg II systems (W0 . 1 Å) than with strong (W0 & 2
Å) systems. From their bias ratio they derive absorber masses, and find that stronger systems
occur in galaxies associated with less massive dark-matter halos (M ∼ 1011 M⊙ ) than weaker
systems (M ∼ 1012 M⊙ ). The Bouche et al. (2007) data, however, reaches only W0 = 0.3 Å,
while with our technique we probe much deeper in rEW. In fact, from our results it follows
just the opposite, namely that the stronger systems correlate more strongly with galaxies:
strong systems in our sample show more clustering with clusters than weak systems. This
apparent contradiction becomes even more evident if one considers that LRG should flag
clusters. But, as already stated, W0 < 0.3 Å systems, might occur in much less massive
(dwarf) galaxies that were not probed in that study. Certainly a natural follow-up of the
present study will be to indentify the absorbing galaxies from the RCS images and look for
W0 − L correlations.
Finally, let us note that rEW is basically a measure of the velocity spread (Ellison
2006). One possible contribution to the overdensity of strong systems observed in clusters
could be that cluster absorbers have larger spreads due to galaxy interactions, which is
much more probable than for the field absorbers. Indeed this effect has been proposed for
’ultra-strong’ absorbers (W0 > 2.7 Å; Nestor et al. 2007). In addition, a mild correlation
between absorber assymetries and rEW has been found in the field (Kacprzak et al. 2007)
that could be strenghtened in our sample due to galaxy interactions. The few cases in our
high-resolution sample S1 that show resolved systems separated by several 100 km s−1 , all
are weak systems. On the other hand, the few strong systems that are both in S1 and S2
do not show particular kinematics when observed at high resolution (e.g., velocity spans of
several 100 km s−1 ). Clearly, a larger sample of strong cluster absorption systems must be
analyzed at high spectral resolution.
8.5.
Limits on the fraction of neutral gas in clusters
Regardless of what produces the observed overdensity of Mg II in clusters, we can
put constraints on the contribution of the absorbing gas to the budget of cold baryons in
clusters. With its low ionization potential of 15 eV, Mg II is a good tracer of neutral gas.
Indeed, several surveys have shown that W0 > 0.6 Å Mg II systems frequently occur in DLA
and sub-DLA systems, i.e., in gas that is predominantly neutral (Rao & Turnshek 2000;
Rao, Turnshek & Nestor 2006). Since ionization corrections are negligible and since column
densities in excess of 1020.3 cm−2 (the definition threshold of a DLA system) can be obtained
easily in low-resolution spectra, measurements of the incidence of DLA systems have led
to robust estimates of the cosmological mass density of neutral gas, ΩDLA . At low redshift
(zabs < 1.6), where confirmation of the DLA troughs at λ = 1215 Å requires space-based
observations, Rao, Turnshek & Nestor (2006) have searched for DLA systems using Mg II
(redshifted to optical wavelengths) as a signpost. By measuring H I column densities directly,
these authors have found that ≈ 50% of Mg II systems with 2 < W02796 < 3 Å are DLA
systems (with average column densities hN(H I)i = 3.5 ± 0.7 × 1020 cm−2 ). According to
these surveys (see also Rao & Turnshek 2000), the mass density provided by DLA systems
at hzi = 0.5 is similar to the high redshift value, ΩDLA = 1 × 10−3 . For a universal baryon
density of Ωb = 0.044 (Spergel et al. 2006), 2.3 % of the baryons in the Universe at z = 0.5
is in DLA systems (at z = 0 this fraction falls down to 1%; Zwaan et al. 2003).
An overabundance of strong Mg II systems of ≈ 10, as observed in our cluster sample,
with a 50% chance of being a DLA system implies a factor of 5 more neutral gas than the
cosmic average. However, assuming overdensities (by mass) of over two orders of magnitude
at the typical cluster radii probed here, r200 , yields a tiny 0.1% of the cluster baryons in
form of neutral gas. This small amount of neutral gas seems more consistent with that in
present-day groups according to H I 21 cm surveys (e.g., Pisano et al. 2007; Zwaan et al.
2003; Sparks, Carollo, & Macchetto 1997). If, as argued for DLA systems (e.g., Wolfe et
al. 2004), the neutral gas has served as fuel for star formation, then the small fraction of
neutral gas in the RCS clusters probed here may be taken as evidence that star-formation
either occurred at much earlier epochs than probed here hzi = 0.6 or it was suppressed by
the cluster environment early in the accretion stage.
8.6.
Speculations
The flattening of the rEW distribution we observe in clusters represents a qualitative
difference with the field in terms of absorber populations. This difference strongly suggests
that it is the cluster environment that drives the morphological evolution of cluster galaxies,
and not the field population accreted by the clusters. If not, clusters would be more efficient
in accreting strong absorbers, which seems unlikely. Instead, it is more likely that galaxies
giving rise to weak absorbers have lost gas due to the cluster environement.
The differing rEW distribution we observe in clusters could be also partly due to a
mix of evolutionary and morphological effects. Studies using imaging stacking have shown
(Zibetti et al. 2007) that strong absorbers arise in bluer, later-type galaxies and weaker
systems in red passive galaxies. If this holds in our sample, it also fits well with our finding
of a flat rEW-distribution, considering that early-type galaxies in clusters evolve less rapidly
than later-type ones (Dressler et al. 1997).
As already stated, local cluster galaxies show a deficit of H I as a function of distance
to the cluster centers. Already at d ∼ 1 Mpc, H I disks do not exceed the optical radii
(e.g., Bravo-Alfaro et al. 2000). If our sample includes the high-redshift counterparts to
these galaxies, the lack of weak Mg II overdensity may indicate that the processes giving
rise to the stripping of gas were already in place at z ≈ 0.6. On the other hand, the denser
gas (including molecular gas; Vollmer et al. 2005) survives the passages through the cluster
center. Using the above argument again, this gas, more internal to the galaxies, may host
the strong absorbers we believe track the galaxy overdensities.
9.
Outlook
We believe the present work opens a couple of important prospects, both from the
absorption-line and the host-galaxy perspectives. First, the high-resolution data can be used
to perform further tests for the cluster environment. Are the ionization conditions the same
as in field Mg II systems? Does the kinematics of strong absorbers give any hint of galaxygalaxy interactions? Indeed, higher-ionization species such as C IV and O VI would perhaps
be better suited for such tests (Mulchaey 1996), but they require space-based observations.
Secondly, the galaxies giving rise to the observed Mg II in clusters must be identified and
their properties compared with the field. Such a comparison should give important clues
about the location of field Mg II absorbers.
Our experiment can be repeated with RCS-2, which will provide 10× more clusters, and
also better photometric redshifts. With a larger sample one could study possible evolutionary
effects. For instance, is there an absorption-line equivalent of the Butcher-Oemler effect?
And, last but not least, the role of gravitational lensing must be further explored, specially
its possible effect on the quasar luminosity function of cluster-selected samples.
We would like to thank Jason X. Prochaska and Sara L. Ellison for important comments
made on an earlier version of this paper. SL, LFB, PL and NP were partly supported
by the Chilean Centro de Astrofı́sica FONDAP No. 15010003. SL was also supported
by FONDECYT grant No 1060823, and LFB by FONDECYT grant No 1040423. The RCS
project is supported by grants to HY from the National Science and Engineering Research
Council of Canada and the Canada Research Chair Program. This research has made use
of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion
Laboratory, California Institute of Technology, under contract with the National Aeronautics
and Space Administration. Funding for the SDSS and SDSS-II has been provided by the
Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation,
the U.S. Department of Energy, the National Aeronautics and Space Administration, the
Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding
Council for England. The SDSS Web Site is http://www.sdss.org/.
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Table 1. High-resolution spectroscopic quasar observations.
Quasar
g-mag
Exposure Time
S/Na
Date
CTQ414
022157.81+000042.5
022239.83+000022.5
022300.41+005250.0
022441.09+001547.9
022553.59+005130.9
022839.32+004623.0
CXOMP J054242.5-40
RXJ0911
Q1120+0195(UM425)
4974Ab
HE2149-2745A
0918Ab
231500.81-001831.2
231509.34+001026.2
231658.64+004028.7
231759.63-000733.2
231958.70-002449.3
232030.97-004039.2
17.0
18.7
18.5
18.7
18.9
19.1
19.0
18.9
18.8
15.7
19.3
16.8
18.2
18.9
17.7
18.7
19.2
18.6
18.9
4500
7200
7200
4500
7200
3400
9900
16200
43200
12900
11600
5400
7200
7200
7200
7200
7200
7200
9000
19
19
20
24
15
10
10
13
51
107
8
35
15
18
33
13
10
15
8
Sept. 29 2006
Sept. 24 2006
Sept. 23 2006
Sept. 24 2006
Sept. 29 2006
Sept. 30 2006
Sept. 30 2006
March 18,19 2006
UVES Archive
March 18,19 2006
Sept. 23, 24 2006
Sept. 29 2006
Sept. 23 2006
Sept. 29 2006
Sept. 24 2006
Sept. 29 2006
Sept. 24 2006
Sept. 23 2006
Sept. 30 2006
a
Median signal-to-noise per pixel.
b
Newly discovered quasars. Named after Chandra fields.
Table 2. Mg II Systems.
LOS
Quasar
zem
zEW
zabs
W02796 [Å]
σW 2796 [Å]
(1)
(2)
(3)
(4)
(5)
(6)
(7)
1.29
1.04
*
*
0.99
*
*
*
1.25
1.20
*
*
*
*
1.82
*
*
*
1.29
1.44
2.80
*
*
*
1.47
1.50
*
2.03
*
*
*
*
*
1.94
*
1.32
*
0.85
1.05
1.15
1.89
*
*
1.72
2.42
0.224
0.237
*
*
0.221
*
*
*
0.212
0.224
*
*
*
*
0.383
*
*
*
0.340
0.353
0.190
*
*
*
0.203
0.415
*
0.211
*
*
*
*
*
0.237
*
0.225
*
0.209
0.286
0.382
0.228
*
*
0.355
0.350
0.3162
0.5919
0.9812
0.4190
0.6815
0.8207
0.7768
0.7746
0.9493
1.0554
0.9395
0.6146
0.3785
0.2503
1.2253
1.0945
0.7494
0.6816
0.6542
1.0160
0.7684
0.7747
0.9946
1.2100
0.2476
0.7320
0.4527
0.6008
0.6028
0.4460
0.4086
0.5139
1.0184
1.6055
1.6105
0.5068
0.5040
0.4470
0.4142
0.6010
0.4154
0.4067
0.8460
0.6980
0.9710
0.484
0.069
0.076
0.030
0.695
0.118
0.122
0.150
0.043
0.881
0.080
0.181
1.181
0.732
0.177
1.685
0.159
0.333
0.597
0.414
0.020
0.033
0.052
0.126
0.540
0.388
0.115
0.175
0.015
0.016
0.228
0.028
0.219
0.661
0.050
0.063
0.148
1.758
0.137
0.109
0.192
0.151
2.028
0.313
1.610
0.022
0.008
0.009
0.009
0.010
0.024
0.008
0.008
0.010
0.036
0.020
0.016
0.043
0.037
0.032
0.065
0.015
0.019
0.016
0.055
0.002
0.002
0.002
0.002
0.005
0.027
0.023
0.006
0.004
0.005
0.008
0.003
0.013
0.021
0.010
0.009
0.009
0.009
0.015
0.016
0.021
0.017
0.024
0.012
0.100
1
2
CTQ414
022157.81+000042.5
3
022239.83+000022.5
4
5
022300.41+005250.0
022441.09+001547.9
6
022553.59+005130.9
7
8
9
022839.32+004623.0
CXOMP J054242.5-40
RXJ0911.4+0551
10
11
Q1120+0195(UM425)
4974A
12
HE2149-2745A
13
0918A
14
231500.81-001831.2
15
16
17
18
231509.34+001026.2
231658.64+004028.7
231759.63-000733.2
231958.70-002449.3
19
20
232030.97-004039.2
022505.06+001733.2
0
Table 2—Continued
LOS
Quasar
zem
zEW
zabs
W02796 [Å]
σW 2796 [Å]
(1)
(2)
(3)
(4)
(5)
(6)
(7)
21
22
23
24
25
26
27
28
29
30
31
092142.03+384316.1
092216.62+384448.0
092746.94+375612.2
092850.88+373713.0
131623.99-015834.9
141604.55+541039.6
141635.78+525649.4
141738.54+534251.1
141838.36+522359.3
141905.17+522527.7
142043.68+532206.3
32
33
34
35
36
37
38
142106.86+533745.1
231710.78+000859.0
231912.83+002046.6
232001.05-005450.5
232007.52+002944.3
232133.76-010645.
232208.09+005948.3
2.34
0.59
1.31
1.45
3.00
1.49
1.38
2.58
1.12
1.61
1.72
*
1.86
1.68
1.23
1.69
0.94
1.98
1.47
*
0.350
0.350
0.350
0.350
0.350
0.350
0.350
0.350
0.350
0.350
0.350
*
0.350
0.350
0.350
0.350
0.350
0.350
0.350
*
0.4730
0.5880
0.7780
1.3310
1.3140
1.0310
0.6980
0.7280
1.0230
0.4920
0.7650
1.6980
0.8510
1.7970
1.1400
1.4220
0.9090
1.5200
1.1950
1.4100
1.760
1.080
2.370
3.320
1.170
1.790
2.640
1.580
1.470
1.120
1.570
1.900
1.800
2.140
1.560
2.440
1.240
1.220
2.480
2.520
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0.100
0
Note. — Table columns: (1) Line-of-sight Numbering [LOS 1–19: Absorbers found in
sample S1; LOS 20–31: Absorbers found in sample S2]; (2) Quasar Name; (3) Emission
redshift; (4) Minimum redshift for a 3σ detection of the Mg II λ2796 line with W >
W0min ; (5) Mg II absorption redshift; (6) and (7) Rest-frame equivalent width of Mg II
λ2796 in Å and 1σ error.
Table 3. Galaxy Clusters.
LOS
(1)
Cluster
(2)
1
2
3
group/cluster
RCS022200+0000.1
RCS022239+0001.7
RCS022221+0001.1
RCS022302+0052.9
RCS022253+0055.1
RCS022443+0017.6
RCS022436+0014.2
RCS022431+0018.0
RCS022449+0016.2
RCS022454+0013.3
RCS022546+0050.0
RCS022556+0052.7
RCS022553+0052.5
RCS022602+0055.5
RCS022558+0051.8
RCS022828+0044.9
RCS022829+0045.8
RCS022832+0046.5
RCS022841+0044.9
RCS022844+0047.7
054240.1-405503
[BGV2006] 015
[BGV2006] 018
RX J0911+05
UM425
MS2137.3-2353
group/cluster
CLJ2302.8+0844
RCS231515-0015.6
RCS231506-0018.1
RCS231501-0013.6
RCS231515-0015.8
RCS231459-0018.9
RCS231512-0020.1
RCS231509+0012.1
RCS231725+0036.6
RCS231755-0011.3
RCS231947-0028.3
RCS231944-0027.0
RCS231944-0026.8
RCS231958-0023.2
RCS231958-0025.1
RCS232028-0043.0
RCS232029-0038.1
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
zcluster
(3)
0.500a
0.270
0.502
0.270
0.509
0.939
0.431
0.173
0.480
0.818
0.511
0.873
0.928
0.423
0.352
0.701
1.032
0.774
0.629
0.271
0.516
0.634b
0.502b
0.527b
0.769c
0.770d
0.313e
0.700a
0.722f
0.566
0.560
0.557
0.496
0.522
0.517
0.420
0.266
0.573
0.651
0.805
0.844
0.796
0.789
1.085
0.589
zmin
(4)
zmax
(5)
d [arcmin]
(6)
0.400
0.237
0.402
0.221
0.409
0.839
0.331
0.224
0.380
0.718
0.411
0.773
0.828
0.383
0.383
0.601
0.932
0.674
0.529
0.340
0.416
0.624
0.492
0.517
0.759
0.760
0.303
0.600
0.712
0.466
0.460
0.457
0.396
0.422
0.417
0.320
0.286
0.473
0.551
0.705
0.744
0.696
0.689
0.985
0.489
0.600
0.370
0.602
0.370
0.609
1.039
0.531
0.273
0.580
0.918
0.611
0.973
1.028
0.523
0.452
0.801
1.132
0.874
0.729
0.371
0.616
0.644
0.512
0.537
0.779
0.780
0.323
0.800
0.732
0.666
0.660
0.657
0.596
0.622
0.617
0.520
0.366
0.673
0.751
0.905
0.944
0.896
0.889
1.185
0.689
0.19
5.99
1.37
4.59
0.56
2.93
1.96
1.88
3.33
2.07
4.07
2.27
1.48
1.00
4.57
1.30
2.98
2.51
1.82
1.50
1.85
3.70
3.70
2.90
0.70
0.10
1.95
0.18
1.50
4.58
1.59
4.92
4.49
0.52
3.43
1.77
7.70
3.92
4.52
4.28
4.01
1.59
0.31
2.51
2.50
d [h−1
71 kpc]
(7)
69.6
1475.5
499.6
1130.9
208.1
1390.2
656.4
328.2
1188.6
941.3
1503.6
1052.1
700.6
332.6
1349.7
557.7
1450.7
1118.7
743.8
371.7
685.6
1519.8
1353.1
1088.4
311.3
44.5
532.6
77.2
651.1
1782.4
614.2
1901.2
1631.9
195.3
1275.2
583.3
1876.6
1536.7
1879.1
1934.4
1840.3
716.9
141.1
1234.6
990.7
Table 3—Continued
LOS
(1)
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Cluster
(2)
zcluster
(3)
zmin
(4)
zmax
(5)
d [arcmin]
(6)
RCS232027-0042.7
RCS022443+0017.6
RCS022527+0015.2
RCS022454+0013.3
RCS022449+0016.2
RCS092148+3841.2
RCS092130+3843.8
RCS092123+3836.3
RCS092131+3845.6
RCS092223+3842.0
RCS092219+3846.1
RCS092222+3841.4
RCS092809+3754.8
RCS092753+3755.5
RCS092811+3756.3
RCS092743+3800.2
RCS092742+3759.2
RCS092731+3754.3
RCS092740+3756.9
RCS092901+3738.6
RCS092843+3741.7
RCS092905+3739.5
RCS092843+3734.6
RCS092851+3733.7
RCS131627-0157.6
RCS141601+5410.4
RCS141617+5407.3
RCS141546+5407.8
RCS141627+5256.8
RCS141749+5341.4
RCS141756+5344.3
RCS141724+5342.7
RCS141803+5223.1
RCS141838+5225.7
RCS141824+5228.0
RCS141840+5221.8
RCS141946+5223.3
RCS141923+5228.5
RCS141838+5225.7
RCS141824+5228.0
RCS142018+5322.3
RCS142111+5339.8
RCS231711+0012.5
RCS231924+0023.1
RCS231923+0020.5
0.853
0.431
0.345
0.511
0.818
0.961
0.373
0.285
0.519
0.501
0.598
0.434
0.441
0.844
0.569
0.540
0.875
0.768
0.773
0.882
0.368
0.640
0.755
0.769
0.897
1.387
0.943
0.698
0.687
1.384
0.378
0.649
0.271
0.614
0.328
0.838
0.337
0.400
0.614
0.328
1.147
0.825
0.521
0.908
0.285
0.753
0.350
0.350
0.411
0.718
0.861
0.350
0.350
0.419
0.401
0.498
0.350
0.350
0.744
0.469
0.440
0.775
0.668
0.673
0.782
0.350
0.540
0.655
0.669
0.797
1.287
0.843
0.598
0.587
1.284
0.350
0.549
0.350
0.514
0.350
0.738
0.350
0.350
0.514
0.350
1.047
0.725
0.421
0.808
0.350
0.953
0.531
0.445
0.611
0.918
1.061
0.473
0.385
0.619
0.590
0.590
0.534
0.541
0.944
0.669
0.640
0.975
0.868
0.873
0.982
0.468
0.740
0.855
0.869
0.997
1.487
1.043
0.798
0.787
1.484
0.478
0.749
0.371
0.714
0.428
0.938
0.437
0.500
0.714
0.428
1.247
0.925
0.621
1.008
0.385
2.30
5.43
6.07
5.01
4.18
2.35
2.33
7.82
3.13
3.05
1.40
3.57
4.73
1.41
4.82
4.08
3.22
3.61
1.49
2.48
4.74
3.65
2.93
3.43
1.18
0.48
3.78
3.87
1.19
2.18
3.06
2.04
5.40
1.72
4.52
2.22
6.72
4.11
4.09
6.65
3.70
2.23
3.51
3.64
2.58
d [h−1
71 kpc]
(7)
1060.0
1820.9
1770.4
1850.0
1902.4
1123.3
714.1
1999.0
1165.5
1115.5
559.5
1201.1
1607.4
647.6
1881.5
1548.8
1495.2
1605.9
665.0
1157.5
1440.7
1507.0
1295.9
1525.7
550.8
244.6
1795.4
1658.0
504.6
1112.3
946.6
844.8
1333.4
695.8
1273.7
1018.8
1930.6
1317.9
1653.9
1873.0
1841.2
1014.9
1309.6
1713.1
658.9
Table 3—Continued
LOS
(1)
Cluster
(2)
zcluster
(3)
zmin
(4)
zmax
(5)
d [arcmin]
(6)
35
RCS232013-0053.2
RCS232016-0056.7
RCS231952+0028.4
RCS232148-0104.1
RCS232158+0100.3
RCS232157+0100.2
RCS232206+0101.6
0.835
0.695
0.569
0.732
0.684
0.856
0.661
0.735
0.595
0.469
0.632
0.584
0.756
0.561
0.935
0.795
0.669
0.832
0.784
0.956
0.761
3.54
4.23
3.94
4.57
2.58
2.57
1.86
36
37
38
d [h−1
71 kpc]
(7)
1619.9
1807.4
1539.8
1994.4
1096.0
1187.7
780.1
Note. — Table displays only lines-of-sights with detected absorption.
Note. — Table columns: (1) Line-of-sight Numbering (same as in Table 2); (2) Cluster Name; (3) Cluster Redshift [references other than the RCS are: a Faure et al. (2004),
b Barkhouse et al. (2006), c Kneib, Cohen & Hjorth (2000), d Green et al. (2005), e Stocke et
al. (1991), f Perlman et al. (2002)]; (4) and (5) Minimum and Maximum redshift surveyed,
respectively; (6) and (7) Projected distance in arcminutes and physical distance at zcluster ,
respectively, from quasar line-of-sight to cluster coordinates.
Table 4: Statistical Samples.
Quasars
SDSS-RCS
S1
S2
S2-best
zmin zmax
0.20 ...
0.20 0.90
0.35 0.90
0.35 0.90
#
190
19
144
88
Clusters
Pairs
#a hBgc i
368
...
46
327
255 263
104 488
#a ∆zcluster
442
...
46
6.32
375
57.01
125
18.06
Note.—These samples are not disjoint.
a
Number of objects having zmin − δz < zcluster< zmax + δz
b
Total number of systems with W > W0min
Absorbers
W0min[Å]
...
0.05
1.0
1.0
#b
...
37
23
14
Table 5: Redshift Path Density of Mg II in Clusters at hzi = 0.6.
Sample ∆zcluster a W02796 [Å] Nhits a
(dN/dz)c b
(dN/dz)f c Overdensity δ
−1
d < 2 h71 Mpc
S1
S1
S1
S2
S2
S2
S2-best
S2-best
6.32
6.32
6.32
57.01
57.01
57.01
18.06
18.06
[0.05, 0.3]
> 0.3
> 0.6
> 1.0
> 2.0
[2.0, 3.0]
> 1.0
> 2.0
5
6
4
9
3
3
5
2
0.79(0.31,1.67)
0.95(0.41,1.88)
0.63(0.22,1.45)
0.16(0.09,0.29)
0.05(0.02,0.14)
0.053(0.015,0.141)
0.28(0.11,0.58)
0.11(0.02,0.35)
d < 1 h−1
71 Mpc
1.09
0.68
0.42
0.16
0.040
0.033d
0.16
0.040
0.7
1.4
1.5
1.0
1.3
1.6d
1.8
2.8
S1
S1
S1
S2
S2
S2
S2-best
S2-best
3.33
3.33
3.33
14.13
14.13
14.13
5.51
5.51
[0.05, 0.3]
> 0.3
> 0.6
> 1.0
> 2.0
[2.0, 3.0]
> 1.0
> 2.0
4
1.20(0.41,2.75)
6
1.80(0.75,3.51)
4
1.20(0.41,2.75)
7
0.50(0.23,0.93)
3
0.21(0.06,0.55)
3
0.212(0.058,0.549)
4
0.73(0.25,1.66)
2
0.36(0.06,1.14)
d < 0.5 h−1
71 Mpc
1.09
0.68
0.42
0.16
0.040
0.033d
0.16
0.040
1.1
2.6
2.9
3.1
5.3
6.4d
4.5
9.1
S1
S1
S1
S2
S2
S2
S2-best
1.45
1.45
1.45
3.72
3.72
3.72
0.79
[0.05, 0.3]
> 0.3
> 0.6
> 1.0
> 2.0
[2.0, 3.0]
> 1.0
3
2
2
1
1
1
0
1.09
0.68
0.42
0.16
0.040
0.033d
1.9
2.0
3.3
1.7
6.8
8.2d
2.07(0.57,5.35)
1.38(0.25,4.35)
1.38(0.25,4.35)
0.27(0.01,1.28)
0.27(0.01,1.28)
0.269(0.014,1.275)
a
Between z = zmin and z = 0.9
b
Cluster redshift density with 95% confidence limits
c
Field redshift density. W0 > 1 Å cut from PPB06; W0 > 2 and W0 > 0.6 Å cuts from NTR05 using
(dN/dz)f = 1.001(1 + z)0.226 exp[−(W0 /0.443)(1 + z)−0.634 ]; and W0 < 0.3 Å cuts from Churchill et al.
(1999) with (dN/dz)f = 0.8(1 + z)1.3 and a 76.7% downward correction due to their smaller W0min = 0.02 Å.
d
NTR06 find (dN/dz)f ≈ 0.015, implying a factor of ∼ 2.2 higher overdensity in this bin at the > 3σ level.
Table 6. Expected Galaxy Overdensity.
log10 (M/M⊙ )
d < 2 h−1
71 Mpc
d < 1 h−1
71 Mpc
d < 0.5 h−1
71 Mpc
13
14
1.7
10.0
8.2
40.0
34.0
132.0
Fig. 1.— Left: Number of quasar-cluster pairs in the SDSS-RCS sample as a function of
the projected physical distance between cluster and quasar line-of-sight at cluster redshift.
The line is the expectation for constant projected number density of pairs. Right: Redshift
distribution (normalized to maximum frequency) of clusters in the SDSS-RCS sample and
of Mg II absorbers in Prochter, Prochaska & Burles (2006).
Fig. 2.— Diagram of the subset of lines of sight (LOS) toward which Mg II absorption
systems were found. The LOS numbering is the same one used in Tables 2 and 3. LOS up to
19 belong to sample S1; LOS 20 to 38 to sample S2. Quasar emission redshifts are labeled
with asterisks, Mg II absorption systems with circles, and clusters with vertical lines. The
thick lines despict the redshift intervals [zmin , zmax ] around cluster redshifts. These intervals
permit a 3σ detection of Mg II λ2796 lines with W0 > W0min = 0.05 Å in S1 and with
Fig. 3.— Selected Mg II absorption line systems in each of the 19 spectra comprising
the high-resolution sample, S1. Each panel (normalized flux vs. rest-frame velocity in
km s−1 ) shows the strongest Mg II doublet in the spectrum, unless an absorption redshift is
within [zmin , zmax ] of a cluster in the same LOS, in which case that latter system is plotted.
Associated systems (zabs ∼ zem ) were not considered
Fig. 4.— Cluster redshift-path density, gc (W0min, zi ) of the high-resolution sample (S1,
W0min = 0.05 Å, lefthand panel) and low-resolution sample (S2, W0min = 1.0 Å). The thick
line is for LOS-cluster distances d < 2, the thin line for d < 1, and the dotted line for
d < 0.5 h−1
71 Mpc. The vertical dashed lines depict the redshift defined by the rEW detection
thresholds. See § 4.2.2 for more details.
– 48 –
Fig. 5.— Mg II redshift number density binned in the entire range of cluster redshifts for
various W02796 lower limits. The filled circles are from clusters with LOS-cluster distances d <
−1
2 h−1
71 Mpc and the open squares from clusters with d < 1 h71 Mpc (symbols slightly shifted
in the x-axis for more clarity). The errors bars correspond to 1σ. The curves correspond
to the fit by NTR05 to their SDSS EDR data of field absorbers along with 1σ limits. The
top panels show results from sample S1 only (high-resolution spectra; 46 pairs, hzi= 0.550),
while points in the bottom panels were calculated using only the S2 sample (375 pairs;
hzi= 0.625).
– 49 –
Fig. 6.— Equivalent width distribution of Mg II absorbers in clusters (corrected by the
cluster redshift path) vs. Mg II λ2796 rest-frame equivalent width for LOS-cluster distances
−1
d < 2 h−1
71 Mpc (lefthand panel) and d < 1 h71 Mpc. The errors bars correspond to 1σ. Data
points with W0 < 1.0 Å resulted from sample S1 only (high-resolution spectra), while points
at W0 > 1.0 Å resulted from sample S2. The lines are the field expectations. The solid line
is the exponential distribution fitted by NTR06 to their MMT data having W0 > 0.3 Å, and
the dashed curve is the power-law fited by CRCV99 to their HIRES data having W0 < 0.3
Å. The vertical line at W0 = 0.3 Å marks the transition in n(W ) pointed out by NTR06.